Fourier energy spectrum centroid: a robust and efficient approach for shear wave speed estimation in ω-K space

Abstract

<p><em>Objective</em>. The propagation speed of a shear wave, whether externally or internally induced, in biological tissues is directly linked to the tissue's stiffness. The group shear wave speed (SWS) can be estimated using a class of time-of-flight (TOF) methods in the time-domain or phase speed-based methods in the frequency domain. However, these methods suffer from biased estimations or time-consuming computations, and they are especially prone to wave distortions in <em>in vivo</em> cases. In this work, we present a parameter-free, robust, and efficient group SWS estimation method coined as Fourier Energy Spectrum Centroid (FESC). <em>Approach</em>. The proposed FESC method is based on the center of mass in <em>ω-k</em> space. It was evaluated on data from computer simulations with additive Gaussian noise, a commercial elasticity phantom, an <em>ex vivo</em> pig liver, and in vivo biceps brachii muscles of three young healthy male subjects. The FESC method was compared with two 2D frequency-domain methods: Max-fre, which considers phase SWS at the peak of <em>k</em>-space, and Fre-regre, which applies linear regression of phase SWS within a fixed bandwidth. Two additional benchmarks included time-domain methods based on cross-correlation (X-Corr) and Radon Sum transformation (RD). <em>Main results</em>. Statistical results showed that our FESC method and the RD method had comparable accuracy and robustness, outperforming the other benchmark methods. In the simulation and phantom studies, when the signal-to-noise ratio is higher than 25 dB, our FESC showed higher accuracy than RD. In the <em>in vivo</em> study, our FESC method had better repeatability than RD. Furthermore, the proposed FESC method was 100 times faster than the runner-up method, X-Corr, and 3,000 times faster than the least efficient method, RD. <em>Significance</em>. All results indicated that our proposed Fourier-based method shows promise in reliably and efficiently providing reference values for group SWS in homogeneous bulk media.<br></p>